I removed old 8" surface element and terminal block. Some of old wiring had to be cut off because of harding/cracking of old wiring. Stove was 23 years old and this burner was the most frequently used one. I soldered the new and remaining old wires together. I used the shirnk wrap that came with the terminal block to cover the solder joint. I screwed the new terminal block (one screw holds it in place - used same screw from old terminal block that was removed). I finished by inserting the new surface element. Everything works fine. In the next week or two after we use it a while, I will check wiring again to make sure there are no changes. You need to be very careful as it gets very hot under the burner.
First thing to do is to KILL THE POWER. The last thing you want is for two leads feeding power to a range coil burner "hot" when you are working on them. After power is off, I removed the coils and set them aside. The terminals had "fried" apparently from to much cooking with hot oils and having the "over splash" working its way down to where the coils plug into the terminals and over time the oil getting in the terminals causes shorting / frying of the leads / contacts.
Anyway, after removing the heat coils I removed the drip pans and cleaned up the area underneath before working on terminals. I like a clean area when I work. I then unscrewed the "brackets" that house the terminals with a Phillips screwdriver and pulled out the assembly.
To completely remove the assembly I cut with a straight razor the existing heat shrink around the wire nuts (These two had been replaced once before. On first go around, I just cut the terminal assembly off and stripped the wire to attach the new terminals). Then I removed the wire nuts and the old assembly. After that I trimmed the wire to the correct length on the new terminal assembly and checked that the wire from the stove was in good shape. Upon confirming I had a good lead, I connected the new terminal leads to the stove leads and put the heat shrink over the connections. I used a lighter to "shrink" the heat shrink to the new connection (not having a proper heat shrink gun, which most of us don't have, the lighter works well as long as you are careful and do not let the lighter heat up to much. Let the lighter cool (esp. if a plastic disposable type or it will melt and ruin the lighter or burn your fingers).
After that I cleaned the area where the terminal block bracket connects to the stove (it gets a bit gunked up over time) before screwing in the new bracket / assembly in place with my screwdriver.
I gave the drip pans a good cleaning, adjusted the new terminal brackets so they were even / centered, cleaned once more the area under the drip pan and replaced the drip pans. The types of pans I have are one piece with a hole for the heat coil leads to go through.
Before placing the coils back in the terminals I took a strip of medium grade, 220 grit, sand paper (you could use steal wool or small wire brush) and cleaned the terminal leads (the steal end that plugs into the terminal only, careful not to damage the burner). This was needed as the leads had accumulated some residue from the same dynamics that caused the burning / melting of the terminal leads and terminal block. Once the leads were clean I fitted them into the place in the new terminal blocks and drip pan grooves.
Finally I turned back on the breaker to the stove and cranked on the burners to test out the connection and that everything was working A-OK.